By means of such a shaving head unit, which is known from WO 2008/010139, filed in the name of the current applicant, the cap of a shaving element can be pivoted with respect to the base portion to an opened position in order to be able to remove the cut-off hairs from the space for receiving cut-off hairs. Since each cap can be pivoted independently of the cap of another shaving element, the caps can be opened one by one in order to be able to clean each space thoroughly without the risk that the other shaving element and cutter member thereof get contaminated by the cut-off hairs. In the known shaving head unit, the cutter member is associated with the cap in a manner that when the cap is in its opened position, the cutter member remains in its normal operating position relative to the cap. In this way, it is prevented that the cutter member accidentally drops down when the cap is being opened. The cutter member can be inspected and cleaned by flushing water over the cap and the cutter member, for example. However, it has been found out that the cutter member cannot be cleaned sufficiently, which will lead to a reduction of the shaving performance. Furthermore, in case the cutter member is damaged, the cutter member cannot be replaced; instead the whole shaving head unit needs to be replaced.